Slide rule



A. LANGSNER Jan' 17a SLIDE RULE Filed Jim 9. 192e A. LANGSNER Jan. 17,1933.

SLIDE RULE 4 Sheets-.Sheet 2 Filed June 9. 1928 4 Sheets-Sheet 5 A.LANGSNER VSLIDE RULE Filed June 9. v1922s @fija Jan. 17, 1933.

A. LANGSNER Jan. 17, 1933.

SLIDE RULE Filed June 9, 1928 4 Sheets-Sheet 4 iPatented' Jan. 17, 1.933

A UNITED' sTATas ADOLPH LANGSNER, F CHICAGO, ILLINOIS, ASSIGNOR TO UGENEDIELIZGEN (.lOMIAIIilY,l

PATENT OFFICE OF CHICAGO, ILLINOIS, .A CORPORATION 0F DEIAWABE SLIDERULE Application led June 9,

My invention relates in general to slide rules and more particularlylto' Va novel scale arrangement in a slide rule whereby variouscalculations of a specialized nature may be accomplished with a minimumof slide rule manipulation and collateral calculation.

The slide rule of my present invention has special utility infacilitating the time-study of machining operations and numerous other13 industrial calculations and includes certain refinements andimprovements whereby calculations of value to engineers and othersengaged in calculating industrial operations involving the machining ofmaterials, may

15 be accomplished with unusual rapidity.

The slide rule of" my present invention is ot such refinement that oftenwith a single setting of thevrule, several factors relating to themachining of materials may be ac- IO curately determined with a speedand facility not possible with similar devices heretofore provided,which require several settings "and considerable collateral mathematicaldetermination. I have accomplished the present improvement by providingcertain novel scales and scale arrangements whereby the weight per footof bar stock of various materials having various standardcross-sectional configurations may be determined by a single 39 settingof the slide rule and whereby the number of pieces which may be cut froma unit length of stock or conversely the length of stock necessary toproduce a given number of articles in a screw machine may be determinedf5 by a single slide rule setting or reading.

By simplifying the calculation of Weight per foot of stock having agiven cross-section and the number of articles per unit length of stockwhich may be made on a lathe or 43 Yscrevv machine, I am able to reducethe eHort and computations and consequently the time necessary incalculating the costs of performing a number of industrial operations.It will-thus be apparent that my slide rule -is 45 vof Vgreat assistanceto engineers, time-study nien and the like, particularly because it isadapted to perform ordinary slide rule calculations in addition to itsspecialized uses and because it is no larger in point of size 59 than isthe ordinary slide rule.

192s. semi No. 284,130.

In the past, several slide rules have been specially designed to performcalculations of this general type, but all of them have been complicatedand hard to manipulate, consisting of several slides mounted adjacentlyin a frame and none of them have been able to combine their specialslide rule characteristics with the characteristics of an ordinaryslide'rule, being true s ecial purpose slide rules and unable to per ormthe functions of a general purpose slide rule.

An important objectof my present invention is toprovide a slide rule ofstandard size and shape having certain novel scale ar rangementswhereby, in addition to being usable for the determination of problemsinvolving multiplication, division, powers,

roots, etc., in fact, any problem which may Another important object ofmy invention is to provide a slide rule of the class and for thepurposes described which is neat, compact and readily portable withoutsacriicing the accuracy of the rule.

Still another important object of my invention is to provide in alogarithmic slide rule, a novel arrangement of scales whereby variousproduction cost calculations may be accomplished with a'minimum of slideyrule manipulation and various related factors may be determined from asingle slide rule setting, the scale arrangement of my present inventionproviding particularly for the solution of involvedcalculationsfpertaining more particularly ton the various relationshipsmaintained as`to Time, Cutting speed, Feed, Length of cut, 1%. P. Mf,the hardness factor of the work material and the diameter of the workpiece or of the cutting tool, in the cutting or machining of materials.l

Still another important object of the invention is to provide a novelandimproved slide rule construction whereby the parts may be accuratelypositioned in order that the body may grip the slide evenly at allpoints in its line of travel and whereby the frictional engagement ofthe body on the slide mfay be quickly, easily and positively adjusted.

Another important object of my' invention is to provide a novelmicrometer adjustment for slide rules wherebythe frictional engagementof the slide in the body may be accurately controlled to the end thatthe slide may be quickly and easily placed in the best working conditionno matter what weather conditions, which may cause the slidle to stickor to slide too freely, may prevai Numerous other dbjects and advantagesof the invention will be apparent as it is more fully understood fromthe following description which, taken in connection with theaccompanying drawings, discloses a preferred embodiment'of theinvention.

Referringto the drawings:

Figure 1 is a top plan view of a slide rul embodying a novel slideadjustment of my invention, parts of the illustration being shown 1ncross-section to reveal the details of construction; f

Figure 2 is an elevation of the slide rule.

shown in Figure l;

Figure 3 is a vertical cross-section taken substantially along the line3-3 of Figure 1; Figure 4 is a view in partial section takensubstantially along the line 4 4 of Figure 3; Flgure 5 is-a top planview of the relatively movable scale surfaces of a slide rule andshowing a scale arrangement of my invention;

Figure 6-is a preferred arrangement or modification of the scalearrangement of myY invention; and v Figure 7 is a preferred formillustrating an improvement of the scale arrangements illustrated inFigures 5 and 6 whereby a new scale, adapted to increase the generalpurpose utility of the slide rule, may be added without increasing thesize of the slide rule.

To illustrate my invention I'shave shown on the drawings, in Figures 1,2, 3 and 4, a slide rule construction comprising a body 11, a slide 13relativel movable in the body and means for adjustln the grip of thebody upon the slide where y the frictional engagement between therelatively movable parts may be varied in order to attain greateraccuracy in the manipulation of the slide rule. In the embodimentillustrated, the body comceive the slide 13 between their opposingsurfaces, being provided with grooves 25 `spaced relationship and are'adapted to readapted to receive projecting flanges 27v formed lin Atheedges of the slide. The outer surfaces of the strips 21and 22 areprovided with runner grooves 23 adapted to receive the inturned flangesof a slide rule runner 81 which may be of any preferred form orconstruction. The upper edge of the lbase strip 15 is mitered andprovided with a diagonal scale surface 29 providing a straight edge 30at its uppermost portions.

after refer to as slide retaining strips are mounted in spacedrelationship on the base 15 and carry scale surfaces 31 and 32 securedto their upper faces. These scale surfaces are adapted to receive scalesand indicia forming various yarrangements. of logarithmic scales. Theslide 13 also is provided with scale surfaces 35 and 37 which aresecured respectively to the upper and' lower faces of the slide. Thesesca'le y surfaces are also .adapted to receive scales and indiciaforming various arrangements of scales adapted to be used' incombination with the scales formed in the scalesurfaces 31 and 32.

`rlhe slide retaining strip 21, in the present instance, is securedfirmly along the lower edge of the base 'strip 15. This may beaccomplished in any convenient manner such as by gluing, riveting or thelike and, in order to provide for the adjustment of the spacing of theslide retaining strips 21 and whereby their frictional engagement withthe slide may be increased or diminished at will, Ihave provided anarrangement for mounting the upper slide retaining strip 22 adjustablyto the base strip 15 and for co-ntrolling its position with respect tothe base strip by means of threaded operating members 59 whereby `amicrometer adjustment of the spacing of the slide retaining strips maybe accomplished. In the embodiment illustrated, the slide retainingstrip 22 is secured to the base strip 15 at three points by means ofpegs 39 which are driven through the strip 22 at its central portion andat points spaced from its ends. These pegs are driven through the strip22 from its upper surface before the scale surface 32 is fastenedthereto as aforesaid. The pegs are provided at their upper ends withears 41 which are adapted to be forced into the material of the strip inorder to prevent relative rotation of the pegs therein. The lower end ofeach peg protrudes from the strip 22 and is housed in a 85 The strips 21and 22, which I will hereini Lea-1,2%

substantiallyfoval aperture formed in the base strip 15 with its longaxis extending l'aterally in the strip, that is to say, normally of theaxis of the strip. A washer 47 having an oval aperture therein similarin size and shape to the cross-sectional contour of the aperture 45, isarranged in a socket 49 formed around the open end of the aperture 45and its oval aperture forms a continuation of the aperture 45, theWasher being held in place by a projecting lug 51 which is arranged toseat in a groove 53 formed in the body of the strip 15. The end of eachpeg 39 extends through the washer 47 and is provided with a. retainingwasher 55 which is secured to the end of the peg by riveting the end 57of the peg over the washer. In this manner the strip 22 is securedfirmly to the strip 15 but'may be moved laterally thereon, the ovalshape of the apertures 45 permitting the pegs 39 to move relativelytothe strip 15 along paths perpendicular to the axis of the strip. Inorder to provide an accurate control of such relative movement I haveprovided a diametral threaded aperture43 in the body of each peg 39.Each of these apertures isadapted p to receive the threadedy end 61 ofadjusting members 59 which are housed in channels 63 formed in the bodyof the base strip 15 from the lower edge 77 thereof to the channels 45.Each adjusting member 59 is provided with a slotted end 65 whereby theadjusting members may be rotated. Upon rotation of the adjustingmembers, the pegs,

39 and consequently the strip 22 may be moved laterally of the strip 15and in this manner the spaced relationship between the. slidesupporting' strip 21 and the `V movable slide supporting strip 22 may beaccurately adjusted. In order to prevent. the adjusting members 59- frommoving longitudinally in the channels 63, I have provided, in eachmember 59,..an annular groove 67 adjacent their outer slotted ends 65.These grooves are adapted to receive pins69 which are arranged inchannels or housings 71 each of which are formed in the base strip 15 atright angles toy a channel 63 and opening thereinto in such a mannerthat when a pin 69 is arranged in position, it will engage the groovedportion 67 Vof a member 59 and prevent the axial movement of said memberin its channel 63. The inner ends of the pins 69 extend into the strip21, being housed in sockets 73 formed therein whereby to increase thestrength of .the attachment vof the strip 21 to the base strip 15.

It will thus be seen that the device of my invention will provide anextremely accurate control ofthe spaced relationship between the slideretaining portions 21 and 22 whereby the frictional engagement of theslide 13 with the base 11 may be accurately controlled.

" The construction is rugged and simple and at tion lof scales for myimproved slide rule whereby the rule is usa-ble as a special purposeslide rule for solving problems dealing particularly with the machiningof various Vmaterials and also as a general purposeslide rule, I haveprovided novel scales, gauge marks and arrangements of mdlcia comprisinglogarlthmic scales formed in the scale surfaces 31 and32 of the sliderule body and the scale surfaces 35 and 37 of the slide.

Logarithmic scales of the typefirst illustrated and described by Gunterare, of course, well known as are slide rules embodying them and mypresent invention relates more especially to the relative arrangement ofseveral logarithmic scales in a slide rule, whereby a rule havingvaluable characteristics and scope is provided. It should be understoodthat where I use the word logarithmic or logarithm in the followingdescription, I am referring to the common logarithmic system, that is tosay, the logarithmic system to the base 10. It should be understood,however, that my invention is not limited to an application of thecommon logarithmic system but may be applied in other logarithmicsystems. Y.

To illustrate my invention I have shown on the drawings, in Figures 5and 6, two arrangements of logarithmic scales representing preferredforms of 1nyinvention. Both of these arrangements comprise a pluralityof multi-cycle logarithmic scales arranged in the rule so that some ofthe scales are relatively slidable with respect to the others and someof "the scales are relatively inverted with respect to other scales ofthe combination. It should be understood that when I use the termsnormal and inverted scales, I do not necessarily mean scales which runfrom left to right andy vice versa but simply mean that oney scale isrelatively inverted with respect to the other. The scales illustratedare particularly adapted to be'applied in a slide rule o f the ordinarymechanical form and construction comprising a body or fixed portion 11,including two spaced slide retaining portions 21 and 22 having scalesurfaces 31 and 32 arranged on the upper faces thereof and a slide l113carried between said retaining portions and having slide surfaces 35 and37 respectively arranged at the upper or obverse and lower or 'reversewhich ten scales in all appear. Four of these scales are carried on therelatively fixed scale vrangements of logarithmic scales in each of theinitial graduation ofthe second.

surfaces 31 and 32 of the body portion of the slide rule while threescales appear on each of the scale surfaces 35 and 37 of the slide.

For thc ,sake of `convenience I prefer to mark certain of the scaleswhich are adapted to be used togetherl in contrasting colors, and

for this purpose I prefer to use the color red for certain scales'whichare used in conjunction a-nd black for certain other scales. Thisassists in keeping the scales separated and distinguished. In the. upperscale surface 32 of the body of the slide rule illustrated in scale isgraduated from .001 to .10 in re'd andv is labeled F eed in red, whilethe lower scale is graduated from 1 to 100 in black and islabeled A orDiamf in black. In the lower scale surface 31 I have formedtwologarithmic scales, the upper of which comprises a single logarithmicscale and the lower of which ycomprises a double or two-cyclelogarithmic scale.I These scales are of equal length and are aligned inthe slide rule as-to their initial and final unit graduations, both asto each other and with respect to the double or two-cycle logarithmicscales arranged" in the scale surface The upper single logarithmic scaleis graduated from 1 to 10 in black and is designated by D in black,

-while the, lower double logarithmic scale is graduated from 1 to 1,00in black and is labeled Length of cut in black. In the illustratedembodiment, the Feed, Diameter,

l and Length of cut scales run from leftto right, being so-called normalscales. is, however, within the contemplation of my present invention toarrange the Feed, Diameter, and Length of cut scales running from rightto left in the slide rule. In the scale surface 31 I also form a gaugemark in blue which I label F. This mark is formed at a point coincidingwith the 1161 point of the D scale and gauge marks in red are formedrespectively in the scale surface to coincide with the 1.9545 and 6.185points of the D scale. Y

In the illustrated embodiments, the front or obverse scale surface 35 ofthe slide carries three logarithmic scales. These scales are of equallength and of length equal to that of the scales formed'in the scalesurfaces 31 and 32.' These scales also are aligned vertically in theslide, that is to say,.thei`r initial and final graduation 'are invertical registration across the slide. The first or upper scalepreferably comprises a ,double or two-cycle logarithmic scale invertedwith respect to the black.

and Cutting speed scales are inverted with Itv scale, that is to say, ascale directionally simi-- lar to the Feed and Diameter scales, andgraduated from 1 to 100 in red and labeled Time in red. The third andlowermost scale is a double or two-'cycle logarithmic scaled'irectionally similar to the P. M. scale, that is to say, relativelyinverted with respect to the Feed, Diameter, Length of cut, and Timescales, and graduated from 1000 to 1() in black and labeled Cuttingspeed'in It will be noticed that the R. P. M.

respect to the Feed, Diameter, Length of cut, and Time scales. This doesnot necessarily mean that the latter must progress from left to rightwhile the R. P. M. and Cutting speed scales progress from right to left,but the Feed, Diameter, Length of cut, and Time scales may progress fromright to left if the R. P. M. and Cutting speed scales in such caseprogress fromleft to 'right, i. e. are inverteflwith respect tol/the.other scales. The gauge points 7 5 heretofore described as 2formed inthe D scale at the 1.9545 and 6.185 graduations respectively have noconnection with the D scale and are formed therein at these pointsmerely to coincide lslide. s.The It. P. M. scale is in effect two scalesand when used in its black aspect cooperates with the Diameter andCutting speed scales and the gauge points75, while in its red aspectcooperates with the Feed, Length of cut, and Time scales. The R. P. M.scale also acts as a transfer scale in ycomputations involving all ofthe red and black scales.

In calculations pertaining to the machining of materials, it is usualthat two or more factors at least are known. From these the unknownfactors may be calculated. .For example; the-diameter of a cylindricalwork piece to be turned or the diameter of a milling cutter may usuallybe determined by means of calipers, the speed of the machine also may bedetermined by means-of a tachometer. In order to discover the cuttingspeed, it will be necessary to perform the calculation'represented inthe following formula:

Cuttingspeed=a14159xD R- r. M. 1 in which D=diameter of the work pieceor cutter. Similarly to find .the time of any operation, it will benecessary to solve the following formula:

3.14159XDXL FeedXcutting speed" in which D=diameter of the work piece orcutter, F eed=the distance advanced by the cutting tool with respect tothe work piece Time= 2 logarithmic slide rule involves extendedmanipulation of the rule and Where it is necessary to find factors suchas Feed or Length of cut in Formula 2 above, the calculation may involvea large number of consecutive slide rule settings and resetting's withthe consequent danger of inaccuracy during the operations whereby errorsin setting the rule are multiplied. There is also the disadvantage ofhaving to'remember intermediate factors between settings. Where suchintermediate factors involve several settings of the slide rule, it isalmost essential that they be noted on a tablet or memo sheet. I

In the past, several slide rules have'been specially designe toperformcalculations of this general type, but most of them have beencomplicated and hard to operate and some have consisted of severalslidesmouuted adjacently in a frame; none of them have been any materialimprovement over the original logarithmic rule except that the scaleshave been labeled differently to assist the particular calculations forwhich they are adapted.

In such multiple slide rules there is still the' necessity of makingseveral consecutive settings of the slides 1n calculating the var1ousunknown factors from given data; there 1s still the disadvantage ofmultiplying errors through resetting the variousl scales or through thedisturbing of a previously set slide while setting an adjacent slide.The eX-` pense also of producing a multiple-slide rule is relativelylarge depending upon the number of slides involved; and the bulk of sucha rule' often reduces its portability so that it can only convenientlybe used in an oiiice and cannot be carried about in the engineers pocketto be used on the spot where and when most useful.

Also the calculations, for which the rule of my present invention isparticularly well adapted, relate to the rotation Vof a circular memberof known diameter, such, for instance, as the calculation ofthe variousrelated factors in the machining of a work piece on a lathe. Wherea-circular member is being rotated, the revolutions per minute may C3 beexpressed by the following formulae:

Peripheral speed in feet per minute Circumference in feet.

llxPerphernl speed in feet ner minute Circumferenoe in` inches. 12XPeripheral speed in feet per minute 3.14150XDiameter in inches.

n. P. M.-

'IIhis relationship may be expressed as folows:

omls-.Ieripheral speed in feet per minute R. P. M. Diameter in inches.

Where machining is involved, peripheral speed is cutting speed, i. e.,the speed of the relative movement between the work piece and the tool,and the formula may be applied equally to a stationary work piece androtatq ing tool or a rotating work piece'and stationary tool. f In thesame way, a formula expressing time in minutes necessar to perform agiven operation maybe deve oped:

Total length of cnt in feet Cutting speed in feet per minute.

' Length cut in inches o'zmsxmameter in nchsx Feed per revolution ininches.

0.2618XDameter in inchesXR. P. M.

Length cut in inches Feed per revolution in u lchesX R. P. M.

Length cut in inches -2618XDiameter in inches Feed per revolution ininheXCutting speed in feet per mmu e. i

Time- This mathematical relationship may be expressed as-follows:

Time in minutesX Feed per rev. in inchesXCuttinE speod in feet perminute Length cui; in inchesXDiametei'bI work piece in inches= 0.2618

It will bei noticed that the constant 0.2618

`appears in both of the above formulae and that this is the point in theCutting speed and R. P. M. scales opposite which the gauge points arelocated.

On the lower or reverse scale surface 37 of the slide I have formedthree scales, the upper scale comprises a double or two-cyclelogarithmic scale graduated in black from 1i. to 1 to 1 and isdesignated B in black. The lower scale comprises a single logarithmicscale and is graduated in black from 1 to 1 and is designated C inblack. In the B scale I form certain gauge marks as fcllows:

f Gauge pointsmarked O in blue coinciding with the 1055 point;

Gauge points marked H in blue coinciding with the 1102 point;

Gauge points marked S in. blue coinciding with the 1273 point;

Gauge points marked RA in blue coinciding with the 6366 point.

.labeled W in black. This .,VVm scale com:4

prises a plurality of gauge marks formed at.

intervals in the scale and labeled respectively Ar, Lf,

Cr, Bzr, Br, Sr, WIr, CIr, Tr'and Af, the

indicia having r being formed in red andl those having f being formed inblack.

are obtained from the specific These vpoints metals, to-wit: lead,copgravity of various per, bronze, brass, steel, wrought iron, castliron, tin and aluminum, which are commonly used in the machine shop, andrepresent logarithmic ratio factors expressing the relationship betweenthe weight per foot of bar stock made of the materials and acrosse-sectional dimension, the points in red applying to stock havingcircular cross-section while the black marks apply to stock ofrectangular cross-sectional shape. These gauge points are determined asfollows: The Weight per cubic inch of the various metals is firstdetermined. In the present instance these Weights were taken fromstandard tabulations contained in various authoritative handbooks andthe true weight per cubic inch of each metal determined as the averageof the Weightstaken. In this manner the weight per cubic inch was foundto be:

. v Pounds per cubic irich Aluminum .09415 Brass L .30370 Bronze .31950Copper 31969 Cast iron .26605 Wrought iron .28060 Lead .41041 Steel.28277 Tin .26467 The Weight per foot of round bar stock may beexpressed by the following formula:

In which: 4 f

W=weight per foot of round stock, cZ=diameter `of stock in inches,Z==length of stock in inches.

By substitution W-'ll-@xmxmxweight/eubic inch.

In arranging the above for application in a slide rule itis mostconvenient to reduce it to one variable, preferably the diameter, and aconstant as in this Way a constant ratio factor between the diameter andthe Weight mayV be expressed as a gauge point which may be used toenable the weight per foot of round stock of the material involved to beobtained with one slide rule setting. The above formula, therefore,becomes:

W=dl2 9.4248 weight per cubie'inch of material.

4 By extracting square root, this becomes:

1/W=d 1/9.4248Xweight per cubic inch.

Y Substituting in thisformula the weight per cubic inch of steel,.28277, the following is obtained:

JW=d Ls32a The value of a gauge point representing the.

ratio vbetween the square root of the Weight of'a unit length (12inc-hes).of round steel stock and the diameter is found to be 1.6325. Bymultiplying the diameter of the rod by 1.6325 and squaring the productthe Weight per foot `of round steel stock may be obtained. Similarvalues for the other materials may be similarly determined to be:

Aluminum 1.96550 Brass 1.6918 Bronze 1.7352 Copper 1.7358 Cast iron1.5834 Wrought iron 1.6261I `Lead 1.9667 Steel 1.6325 Tin 1.5793

W=fw X 25X 12 X .28277 W=w #X 3.39324 auge point for fiat steel barsThis gives a of 3.39324. Simllar gauge points may be determined for theother materials:

-Aluminum 1.1298 Brass 3.6444 Bronze 3.8352 Copper 3.8352 Cast iron3.1926 Wrought iron.- 3.3672 Lead- 4.9249 Steel 3.3932 Tin 3.1760

These gauge points may be laid out by forming andnverted ysinglelogarithmic'scale R, as indicated in dotted lines in Figure 5, havingits initial and final indices in alignment respectively with the finaland initial indices of the C and D scales and forming gauge marks in thescale in coincidence with the calculated values' enumerated above.

In laying out these eighteen gauge points on .the slide rule, however, Iprefer to use the formula:

Logarithm of the estimated number X length of scale Distance from theright index.

The slide rule illustrated in the drawings is the so-called lO-inclislide rule and measures exactly 250 mms. from the initial to t-he finalunit yindex marks of the various scales formed in the scale surfaces.Substituting in the above formula gives in millimeters the distancesJfrom the right index at which the by applying thel .various gaugepoints should be arranged.

Distance Gauge point fromright- Dea' index UWB-Aluminum (flat) 0. 521695A--Black .15793-Tin (round) 1. 959425 lr--Red 15834-Cast iron (round) 1964513 Ir-Red 16261-Wrought iron (round) 2 078253 WIr-Red 16325-Stee1(round) 2 095038 Sr-Reri 16918-Brass (round). 247500 Br-Rcd 17352-Bronze(round) 2 355831 Br-Red 17352-Coppe1-(round) n 355831 (Jr-Red 19667-Lead(round) 2 891189 Lr-Red 31700-'1111 (hat) 4 039877 If-Black 31926-08512iron (flut) 4 962172 CII-31 aca 33672-Wr0ught iron (flat) 5 189768Wij-1;l k

1 ac 33932-Stee1(at) 5. 222553 Sf-Black (WA4-Brass (fiat) 5.527934B11-Black 38352-Bronze (fiat) 5 746058 Bf-Black 3S352-C0pper (Iiat) f49249-Lead (at) M550-Aluminum (round) By laying off these points asindicated, the W scale may be arranged in the slide i surface midwaybetween the upper and lower edges. To determine the weight per foot ofround stock all thatv is necessary is to set the gauge pointcorresponding to the material involved, opposite the right hand indicesof the rule and on the A or Diam. scale, above the point on the C scalerepresenting the diameter of the bar, read the weight points give acomparison of the area of the section with respect to the area of acircle taken as unity. The ratios adopted are as follows:

Circle =1.000 v. Square :1.27 3 Hexagon =1.102 Octagon 1.055 Rightangle: .6366 These ratios are section factors, that is to say, theweight of a round bar multiplied by the section factor will give theweight of a bar lof equal length and similar material having across-section corresponding to the sec-` tion factor. Havingfound .theweight of a roundbar having a diameter equal tothe side of thesquare,`the shlort diameter of a heXagon, the short diameter of anoctagon, the side of a right angle, depending upon the shape underconsideration, the weight of suchsupposititiousroundbar ismultiplied bythe section factor and the resulting product is the weight of one footof metal ,stock having a crosssecton of the shape under consideration.These gauge points are arranged in the B scale and are spaced thereinrespectively as follows: The O mark. representing Octagon, is arrangedto coincide with the 1.055`point, the H mark, representing hexagon, isarrangedl to coincidewith the 1.102 point, the S mark, representingsquare, is arranged to coincide withy the 1.273 point and the R.A. mark,representing right angle, is arranged to coincide with the .6366 point.These gauge marks are repeated in the second half of the doublelogarithmic scale comprising the B scale.

For a 10-inch (250 mm.) rule these points are arranged in the B scale asper 'the following table:

Point Distance from left indexl M ark 1055 0.114432 inches- O (Octagon)1102 0.207592 inches. H (Hexagon) 0.515897 inches S 3.950131 inches(Square) RA (Right Angle) n e e a second and more desirablemodification,

from certain aspects, of the scale arrangements, as shown in Figure 5,whereby an additional scale is made more fully available for use to theend that the slide rule may be more easily manipulated. Y,

In the modification in Figure 5 it is im? practical from spaceconsiderations to place the IV scale, especially where gauge points fora number of materials otherA than those shownare incorporated in therule, upon the R scale. The R scale by itself is extremely useful and inorder to separate the W and R scales and to simplify the rule, I combinethe Length of cut scale which, in Figure 5, is shown arranged in thelower scale surface 31 of the body of the rule, with the A or Diam scalewhich is in the scale surface 32. Its place in the scale surface 31 istaken by a W scale which is formed in the same manner as ythe -"W scalein the combination illustrated in Figure 5, except that the W lscale ofthe -present combination is inverted with respect to the W scalepreviously described, that is to say. the gauge 4points instead of 4being laid vout from the right index `of the rule, are

face .37 which? in the embodiment illustrated in Figure 5, was occupied'by the W scale,

i5.' I 'have arranged a reciprocal or inverted normal logarithmic scalemarked in black. This scale is of similar length to the C and B scales.vThe addition of the reciprocal or R scale in place of the W scale onthe reverse side of the slide 1s of advantage slnce it eliminatesintermediate slide settings when' multiplicatlon and division of morethan two f factors is undertaken using the C, D and R scales.

It will be apparent that the slide rules embodying my present inventionare adapted, on account of the provision of Feed, Diam, 1%. I). M.,Time, Cutting speed and Length of cut scales, to perform all thecalculations which may involve these quantities and in addition mypresent slide rule may be used to determine the weights of bar stockhaving any one of a number of cross-sectional configurations. and madeof any. one of a number of materlals 1n common use. Since the cost ofperforming a given mechanical operation upon a bar of materialy may beexpressed in terms of the weight of the materialfit is apparent that myimproved slide rule is particularlyfadapted to assist in determining thecost of performing various production operations upon bar stock havingvarious cross-sectional configurations and made of various materials,and to materially reduce the effort in making various necessarycalculations, and all this without destroying the general purposecapacities of the rule.

The gauge mark F heretoforedescribed as-being arranged in the scale D isfor the purpose ofdetermining the number of feet of bar stock requiredto produce a unit number of finished pieces in screw or cut-off machinewhere the length of a required piece and the width of the cut-off toolis known.

` This particular gauge point is present in the the cutting operation;A'In actual practice at least 4 inches are necessary. The standard lengthof bar stock for use in screw machines is 10 feet. If a chuckingallowance of 4 inches is used, a total of 116 inches of stock availableformachining purposes remains, that is to say, only 96.66% of the `barcan be used to produce the complete product, i. e., a chuckingefliciency of .9666. The relationship may be expressed as follows:

In which:

Zl=total length in` feet of stock (10 ft.

Transposing this formula the following proportion is obtained:

constant values assumed, the proportion becomes:

a gauge point F, therefore, should be located at the 1.160 mark of thescale. As stated before, the gauge point F is loc-ated at 16.325 mms.from the left index of the Dscale. This figure is for a standard 10-inchslide rule in which the D scale is exactly 250 mms. in length, and isdetermined by actual measurement', being the distance from the 1.160mark to the nearest unity mark on the scale. From the above it will beapparent that by dividing the length of the piece plus the width of thecut-off tool in inches by 1.160, the number of feet of bar stockrequiredto produc-e 1000 pieces will be indicated. This division may beeasily accomplished by set-y ting the unit index of the C scale oppositethe F gauge point and reading on the C .Scale immediately over thelength of each piece plus the width of the cut-oil' tool on the D scale,the number of feet of bar stock necessary to produce 1000 pieces.

It will be apparent that the slide rule of y l my invention is adapted,in addition toits special purpose capacity to perform nearly all thegeneral purpose functions of an ordinary Mannheim slide rule. The scalearrangements of Figs. 5 and 6 however will not permit the determinationof cubes and cube roots and yI have illustratedin Figure 7 of thedrawings a mea-ns whereby such determinations may be accomplished;

In the bottomedge surface 77 of the slide rule body I form a triplelogarithmic scale labeled E in black. This scale is alignedv in thesurface 7 7 ofthe slide rule body so that its initial and final` unitgraduations register with-theinitial and final unit graduations of the Dscale in the scale surface 31. In connection with this scale, the sliderule runner t;

Aim

sacrificing any of its material advantages, the forms herein describedbeing merely preferred embodiments thereof.

Having thus described my invention, what I claim as new and desire tosecure by Letters Patent is:

1. In a slide rule having relatively movable scale surfaces, scalesformed and arranged in the scale surfaces and including a twocycle loarithmic scale representing Time, a two-cyc e lo arithmic scale meansrepresenting R. P. and Cutting speed, said twocycle scale means beingrelatively inverted with respect to the scale representing Time, saidTime, R. P. M., and Cutting speed scales being formed in relativelystationary scale surfaces, and' two-cycle logarithmic scalesrepresenting Feed, Diameter, and Length of cut formed in scale surfacesrelatively movable with respect to the surfaces containing the Time, R.P. M., and Cutting speed scales.

2. In a slide rule having relatively movable scale surfaces, scalesformed and arranged in the scale surfaces and including a two-cyclelogarithmic scale representing Time, a two-cycle logarithmic scale meansrepresenting R. P. M. and Cutting speed,

sald two-cycle means being relatively inver t. j

ed with respect tol the' scale representing Time, said Time, R. P. M.,and Cutting speed scales being formed in relatively stationary scalesurfaces and two-cycle Alogarithmic scales re resentin Feed, Diameter, land Length o cut, an a gauge mark, reglstering with the .2618 point inthe Cuttingspeed scale when the scales are aligned in central position,formed in'scale surfaces relatively movable with respect to the surfacescontaining the Time, R. P. M., and Cutting speed scales.

3. In a slide rule*having relatively movable scale surfaces, scalesformed and ar- 4. In a slide rule having a pair of relatively movablescale surfaces, a two-cycle logarithmic scale suitably graduated torepresent Feed, and a two-cycle logarithmic scale graduated to representLength of cut; said scales being formed in relatively stationary scalesurfaces, a two-cycle logarithmic scale suitably graduated vto representTime, and atwo-cycle scale relatively inverted with respect to the Feed,Time, and Length of cut' tively slidable parts, one of` which is formedwith means providing two-cycle R. P. M. and Cutting speed scales andtheother of which is formed With means forming a two-'cycle Diameter scalereversed with respect to the R. P. M. and Cutting speed scales and agauge point formed in the rule opposite a .261.8

point in the' Cutting `speed scale when the scale carrying slide ruleparts` are centered with respect to each other.

6. A slide rule including `a pair of relatively slidable parts, one ofwhich is provided with means formin two-cycle scales representing R. P.M. and Cutting speed, and the other of which is provided with meansforming a two-cycle scale relatively inverted with respect to the RPM.and Cutting speed scales Vand having unity graduations registering withthe unity graduations in the other scales when the parts are centeredand with a gauge mark registering with a graduation of.

the Cutting speed scale when the parts are centered, which-saidgraduation has a numerical significance corresponding to themathematical ratio:

Time of operation X Cutting speed X Feed of tool per revolution Lengthof cut taken on Work piece X Diameter of Work piece.

ranged in the scale surfaces and including a pair of single logarithmicscales formed in ascale surface, one of the scales including a gaugepoint representing the specific gravity of a material formed in thescalefsurface with respect to the unity graduation of the scale taken asunity specific gravity, a single Time of operation -X ICuttingfspeed XFeed' of tool per revolution 7. A. slide rule including a pair ofrelatively slidable two-cycle logarithmic scales and a gauge pointarranged in said rule in position to register witha graduation of one ofthe scales, when ,the moving parts of the rule are centered, saidgraduation representing the mathematical ratio Length of cut taken onwork piece X Diameter of Work piece.

logarithmic scale and a doublel logarithmicscale of equal length formedina relatively movable scalesurface whereby the weight lper unit lengthof a rod of the material may e determined by a single slide rulesetting, and a triple logarithmic scale of equal length to the singlescales and adapted to cooperate with a said singlelog scale whereby cuic relationships may be determined.

senting Time, a two-cycle logarithmic scale representing-Length of cut,said lTime and Ifength of cut scales being aranged in relatively movablescale sufaces, means forming a two-cycle logarithmic scale inverted withrespect to the Time and Length of cut scales and graduated to representR. P. M. and formed in a scale surface relatively stationary withrespect to the Time scale, means forming two-cycle logarithmic scalesrepresenting Diameter and Feed, said :Diameter and Feed scales beingeach relatively shiftable with respect to means Yforming an R. P M.scale in the slide rule, a two-cycle logarithmic scale relativelyinverted with respect to the Time and Length of cut scales and graduatedgauge marit formed in an adjacent part of the slide rule relativelyshiitable with respect to the part in which the Cutting speed scalespeed scale,

' tively .spect is formed, said gauge point heing formed in the rule toregister with the .2618 pointin the Cutting speed scale when the same iscentered with respect to the other scales.

, 9. ln a slide rule having a pair of relatively shiitahlescale-carrying parts, a plurality of two-cycle logarithmic scales formedand arranged in said scale surfaces, some of the scales being relativelyinverted with respect to otherlscales formed in the scale carryingparts, said scales being arranged so that a pair of scales, similarlygraduated and representing respectively Length of cut and Time, are enrelatively shizttable parts,` a pair ci scales, representing Feed andDiameter, each formed on a part' oi' the rule relatively shiftable withrespect to another part carrying means forming a logarithmicscalerelatively inverted with respect to the Feed and Diameter scales andgraduated to represent R. P. M., al scale representing Cutting speed torepresent Cutting speed and a ed to represent R. l?. M., a scale reresenting Cutting speed relatively inverted wlth respect l to the Feedand Diameter scales and a cooperating gauge mark on an adjacent partrelatively shiftable with respectto the part carrying the Cutting speedscale, said gauge mark being located opposite the .2618 point 'in theCutting speed scale when the same is centered in the rule with respectto the other scales carried thereon, said Cutting speed .scale beingformed for cooperation 'with the representing Time, a Diameter scalelela-1 tively shiftable with respect to an R.. P. M

scale inverted lwith respect to the Diameter scale, a Feed scalerelatively shiftable with respect to an R. P. M. scale relativelyinverted with respect to the Feed scale, and a Cutting speed scalerelatively inverted with respect to the Diameter scale and relativelyshiftable with respect to a scale carrying part provided with a gaugemark therein, which, when the slide rule parts are (centered, registerswith a graduation on the Cutting speed scale representing the ratio:

Time of operation X Cutting speed X Feed of tool per revolution Lengthof cut taken on work piece X Diameter of Work piece relatively. invertedwith respect to the Feed and Diameter scales, and a cooperating gaugemark on an adjacent part relatively shitable with respect to the partcarryin the Cutting said gauge mark ing located opposite the .2618 pointin the Cutting speed scale when the same is centered in the rule withrespect to .the other .scales carried thereon.

10. `In a slide rule having a pair of relashitable scale-carrylng parts,a plulogarithmic scales formed rality of two-cycle some of andarranUed-m said scale surfaces,

the scales llieing relatively inverted with reto the other scales, saidscales being arranged so that a pair of scales, similarly graduated andrepresenting respectively Length of cut and Time, are on relativelyshitable parts, a pair of scales, representing Feed and Diameter, eachfarmed on a part of the rule relatively shiftable with respect'toanother part carrying means forming a logarithmicscale relativelyinverted with respect to the Feed and Diametenscales and graduatwhichexists in turning operations.

12.. In a slide rule having a pair of cooperating relatively shiftablescale-carrying parts, means forming two-cycle scales of equal length andaligned inv said relatively shiftable scale surfaces when the slide ruleparts are centered, certain of said scales beingrelatively inverted withrespect to t other scales and arranged so that a two-cy e scale,representing Length of cut, has re tively shiftable co-operation withanother two-cycle scale representing Time, a re1atively invertedtwo-cycle scale representing R. P. M. has relatively shiftablecooperation with a two-cycle scale representin Feed, a relativelyinverted two-cycle sca e representing B. P. M. has relatively shiftablecooperation with a two-cycle scale representing Diameter, and arelatively inverted twocycle scale representing Cuttingi speed4 hasrelatively shiftable cooperation with a gauge point located in the ruleat a point opposite the .2618 mark of the Catlin? speed scale when theslide rule is cante` 122 i ase4,ee4

15; of theinverted scale representing the ratio:

of operation X Cutting speed 'X Feed of tool peri-evolution lliengthiofeut taken on work piece X Diameter ofwork piece le'Xistsiin turning oerations.

In witness whereof, I ave hereunto sub- Silibegd my naue.

'l ADOLPH LANGSNER.

